Calculation Examples
Example: longitudinal reinforcement for shear and torsion according to EC2
Given: For the rectangular section of Figure 1 calculate the longitudinal reinforcement for shear and torsion. The section considered has depth 1500mm, width 1000mm, d = 1450mm. The vertical membe...
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Nominal flexural strength of a reinforced concrete beam
Compute the nominal flexural strength Mn of the reinforced concrete rectangular section of Figure 1. Given: fc′ = 5000 psi, fy = 50,000 psi, b = 15 in., d = 22.5 in. and As= 4-#9 bars. F...
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Beams: maximum moment
Find the maximum moment of the above beam which is subjected to triangular vertical load. SOLUTION: ΣΜΒ = 0 → ΑΥ –(1/2)ql(l/3)=0 → ΑΥ = (1/6)ql ΣFY = 0 → ql/6 + BΥ –(1/2)ql=0 → BΥ = (1/3)ql Assum...
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Column in buckling
Consider a universal column 200mm x 200mm with a flange thickness of 10mm and web thickness of 7mm. The height of the column, which is fixed in concrete at its base, is 10m and the load is applied...
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Maximum Factored Vertical Shear
A simply supported beam (Figure) with a span of L=20ft is subjected to a uniform service load of 1200 lb/ft, including self weight, and a live load of 900 lb/ft. Determine the maximum factored...
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Flexular Crack in Concrete Beam
For the simply supported beam of Figure 1, determine the uniformly distributed load, q, at which the flexural crack forms. The beam has a length L=7m, and f’c=25Mpa. Figure 1: Cross-section of Con...
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Calculate the vertical deflection of a beam
Calculate the vertical deflection of the beam (magnitude and direction) at the midpoint of the central span (point A) Solution Use virtual work method: Virtual Structure From Equilibrium: Shea...
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Truss vs Cable
Truss and cable elements are defined by their ability to carry solely axial loads. Nonetheless, since cables have no stiffness when loaded in compression, they function only in tension. Moreover,...
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Spring Assemblies in Series/Parallel: Two Springs in Series
Based on Figure 1, we get: where: In matrix form, the above can be re-written as: Example Figure 2: Two Springs in Series - Example Calculate k1, δ2, and f3. Solution Ba...
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Calculate the variation in length of the rod
The rod of the picture is loaded with the force 2P which is uniformly distributed on Section D where applied. If the material of the rod is homogenous with Elastic Modulus E find the variation in len...
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